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INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS J. Phys. D: Appl. Phys. 38 (2005) 2606–2611 doi:10.1088/0022-3727/38/15/011 Coherent noise-free ophthalmic imaging by spectral optical coherence tomography A Szkulmowska 1 , M Wojtkowski 1 , I Gorczynska 1 , T Bajraszewski 1 , M Szkulmowski 1 , P Targowski 1 , A Kowalczyk 1 and J J Kaluzny 2 1 Institute of Physics, Nicolaus Copernicus University, ul. Grudzia dzka 5/7, PL-87-100 Toruñ, Poland 2 Collegium Medicum, Nicolaus Copernicus University, ul. Curie-Sklodowskiej 9, PL 85-094 Bydgoszcz, Poland E-mail: [email protected] Received 30 November 2004, in final form 20 April 2005 Published 22 July 2005 Online at stacks.iop.org/JPhysD/38/2606 Abstract In this contribution we examine a methodology to avoid parasitic cross-correlation terms in spectral optical coherence tomography (SOCT) images. The optimal conditions of optical power and exposure time are found theoretically and confirmed experimentally to ensure that parasitic images are hidden under the shot noise. An upper limit on useful exposures may then be estimated. In a case of SOCT imaging of the retina this limit is below the ANSI safety limit. 1. Introduction Optical coherence tomography (OCT) is an optical modality, which allows to determine the internal structure of weakly absorbing and scattering objects. The technique relies on an examination of a beam of low coherent light reflected back at the internal interfaces of the layered structure of an object. In order to determine the locations of these interfaces along the path of penetrating beam OCT uses interferometry. The light backreflected within the object is combined with the light reflected from a reference mirror and then is analysed by a detection system. Consecutive measurements with the beam in adjacent transversal positions provide the cross-section of the structure. Because this technique is non-contact, non-invasive and safe for the eyes (as long as exposure is limited to a certain level), the most advanced medical applications of OCT are in ophthalmology for diagnosing and staging of ocular diseases. There are two possible ways in which structural information can be decoded from an interference signal: time domain OCT (TdOCT) [1] and the alternative method of Fourier domain OCT (FdOCT) [2]. The difference between both techniques is in the method in which the structural information is extracted from the signal. In the TdOCT an optical delay line has to be mechanically scanned in order to record a single A-scan (a line in a cross-sectional image). In the fastest systems available, which, alas, do not assure the highest possible resolution, it takes 250 µs to acquire a single A-scan [3]. Nevertheless, this traditional method has demonstrated its usefulness in diagnosing ocular pathologies [4] and has been implemented into commercial instruments—StratusOCT (Carl Zeiss Meditech Inc.) and OCT-Ophthalmoscope (Ophthalmic Technologies Inc.). FdOCT does not require a mechanical scan of the optical delay line because locations of the backreflecting interfaces are encoded in frequencies of fringes superimposed on the spectrum of the light source. This spectrum is registered either by a spectrometer equipped with a CCD camera (spectral OCT, SOCT) [58] or by using a tunable laser as the light source and a photodiode as the detector (swept source OCT) [912]. In both cases information is decoded by inverse Fourier transformation. As the process of registration (i.e. light exposure) and data transfer is separated from the process of decoding, the exposure time per A-scan may be as short as 34 µs[13] for SOCT and 53 µs for swept source OCT [14]. SOCT enables measuring axial image information by parallel registration of different optical frequency components of interfering light waves. When compared with TdOCT, the spectral technique allows better averaging and filtering of noise components. The effective signal-to-noise ratio (SNR) is increased by a factor proportional to the number of pixels in CCD sensor [12, 15, 16]. It has been also shown that SOCT does not require the balance detection to remove random intensity noise even for exposure time as short as 5 µs per A-scan [17]. The sensitivity advantage of SOCT system over TdOCT and 0022-3727/05/152606+06$30.00 © 2005 IOP Publishing Ltd Printed in the UK 2606
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Page 1: Coherent noise-free ophthalmic imaging by spectral optical coherence tomography

INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 38 (2005) 2606–2611 doi:10.1088/0022-3727/38/15/011

Coherent noise-free ophthalmic imagingby spectral optical coherence tomographyA Szkulmowska1, M Wojtkowski1, I Gorczynska1,T Bajraszewski1, M Szkulmowski1, P Targowski1, A Kowalczyk1

and J J Kaluzny2

1 Institute of Physics, Nicolaus Copernicus University, ul. Grudzia�dzka 5/7, PL-87-100Toruñ, Poland2 Collegium Medicum, Nicolaus Copernicus University, ul. Curie-Sklodowskiej 9, PL85-094 Bydgoszcz, Poland

E-mail: [email protected]

Received 30 November 2004, in final form 20 April 2005Published 22 July 2005Online at stacks.iop.org/JPhysD/38/2606

AbstractIn this contribution we examine a methodology to avoid parasiticcross-correlation terms in spectral optical coherence tomography (SOCT)images. The optimal conditions of optical power and exposure time arefound theoretically and confirmed experimentally to ensure that parasiticimages are hidden under the shot noise. An upper limit on useful exposuresmay then be estimated. In a case of SOCT imaging of the retina this limit isbelow the ANSI safety limit.

1. Introduction

Optical coherence tomography (OCT) is an optical modality,which allows to determine the internal structure of weaklyabsorbing and scattering objects. The technique relies on anexamination of a beam of low coherent light reflected backat the internal interfaces of the layered structure of an object.In order to determine the locations of these interfaces alongthe path of penetrating beam OCT uses interferometry. Thelight backreflected within the object is combined with the lightreflected from a reference mirror and then is analysed by adetection system. Consecutive measurements with the beam inadjacent transversal positions provide the cross-section of thestructure. Because this technique is non-contact, non-invasiveand safe for the eyes (as long as exposure is limited to a certainlevel), the most advanced medical applications of OCT are inophthalmology for diagnosing and staging of ocular diseases.

There are two possible ways in which structuralinformation can be decoded from an interference signal: timedomain OCT (TdOCT) [1] and the alternative method ofFourier domain OCT (FdOCT) [2]. The difference betweenboth techniques is in the method in which the structuralinformation is extracted from the signal. In the TdOCTan optical delay line has to be mechanically scanned inorder to record a single A-scan (a line in a cross-sectionalimage). In the fastest systems available, which, alas, donot assure the highest possible resolution, it takes 250 µs to

acquire a single A-scan [3]. Nevertheless, this traditionalmethod has demonstrated its usefulness in diagnosing ocularpathologies [4] and has been implemented into commercialinstruments—StratusOCT (Carl Zeiss Meditech Inc.) andOCT-Ophthalmoscope (Ophthalmic Technologies Inc.).

FdOCT does not require a mechanical scan of the opticaldelay line because locations of the backreflecting interfacesare encoded in frequencies of fringes superimposed on thespectrum of the light source. This spectrum is registeredeither by a spectrometer equipped with a CCD camera (spectralOCT, SOCT) [5–8] or by using a tunable laser as the lightsource and a photodiode as the detector (swept source OCT)[9–12]. In both cases information is decoded by inverseFourier transformation. As the process of registration (i.e.light exposure) and data transfer is separated from the processof decoding, the exposure time per A-scan may be as short as34 µs [13] for SOCT and 53 µs for swept source OCT [14].

SOCT enables measuring axial image information byparallel registration of different optical frequency componentsof interfering light waves. When compared with TdOCT,the spectral technique allows better averaging and filtering ofnoise components. The effective signal-to-noise ratio (SNR)is increased by a factor proportional to the number of pixels inCCD sensor [12,15,16]. It has been also shown that SOCT doesnot require the balance detection to remove random intensitynoise even for exposure time as short as 5 µs per A-scan [17].The sensitivity advantage of SOCT system over TdOCT and

0022-3727/05/152606+06$30.00 © 2005 IOP Publishing Ltd Printed in the UK 2606

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Coherent noise-free ophthalmic imaging by spectral optical coherence tomography

the possibility of high speed imaging, both show the potentialof SOCT to be a powerful tool for ophthalmic imaging.

Cross-sectional images obtained by SOCT may sufferfrom coherent noise parasitic elements, inherent to thistechnique [18, 19], which may lead to misinterpretation ofresultant tomographic images and decrease the SNR. Theseparasitic features are mirror images which result from theFourier transform of a real function (spectral fringes) as wellas false images owing to the cross-correlation between wavesreflected at different interfaces within the object, or at surfacesof the optical elements in the interferometer. It has beenshown that both mirror images and cross-correlation termscan be eliminated by the phase shifting methods [20–25].However, these multiframe techniques require a collection ofmore than one spectral fringe pattern from the same region,taken with a pre-selected additional phase shift in the referencearm. In this method the object must be stationary between themeasurements, to within a fraction of the centre wavelength ofthe light source. The latter makes this technique hard to applyfor clinical studies.

Fortunately, in the case of thin objects (as the retina of theeye) it is easy to sufficiently separate both mirror images toprevent their overlapping. To eliminate the cross-correlationnon-sample dependent terms (so-called background) it issufficient to register the spectral fringe pattern in the absenceof the object and subtract it from the spectrum registered withthe object in the place. The background measurement may beperformed only once per given instrument setting.

The most serious problem in retinal studies is thepresence of the cross-correlations between waves reflectedfrom the inner limiting membrane (ILM) and the retinalpigment epithelium (RPE). The resulting feature may bemisinterpreted as a real morphological structure. This problemarises, paradoxically, as a result of the high sensitivity ofSOCT. Because of this high sensitivity, the SOCT ophthalmicexaminations are performed at an energy (optical powermultiplied by exposure time) about 100-fold lower than inthe traditional TdOCT. It is, therefore, tempting to increaseoptical power to the same safety limit in order to enhancesensitivity. Unfortunately, beneficial results of higher poweron the sensitivity level are counterbalanced by the fact thatsimultaneously some artefacts which were invisible before,now emerge from the shot noise. In this contributionwe analyse theoretically and experimentally, the optimalconfiguration of the SOCT system for retinal imaging to keepcross-correlation artefacts under the noise level.

2. Materials and methods

The SOCT instrument is based on an optical fibre Michelsoninterferometer set-up (figure 1) with a 50/50 directionalcoupler—DC. The light source—LS is a superluminescentdiode emitting at 810 nm with a 20 nm FWHM and the outputpower of 1 mW. The detector is a custom design spectrometerconsisting of a diffraction grating—DG and a 12-bit CCDcamera, with the total efficiency of the spectrometer η = 0.14.The reference mirror—RM is kept in a fixed position.A measurement head in 4-f configuration is used for retinalimaging, where the pivot of the transverse scanner X-Y isimaged via lenses L1 and L2 into the pupil plane of investigated

Figure 1. Optical scheme of the SOCT device. LS—light source,OI—optical isolator, DC—directional coupler, PC—polarizationcontroller, NDF—neutral density filter, RM—reference mirror,X-Y—transversal scanner, DG—diffraction grating, CCD—CCDcamera, L—lens, COMP—personal computer.

eye. For imaging of a model glass plate, the lens L2 isremoved and the lens L1 is placed between the scanner andthe object so that the distances lens–object and scanner–lensare equal to the focal length of the lens. The spectral fringepatterns are registered by the CCD detector and then transferredto a personal computer. The spectral pattern acquired inthe absence of the object is subtracted from each collectedspectrum. The resulting signal is Fourier transformed into anA-scan.

The system operates in the shot noise limited detectionmode with 90 dB of sensitivity. The exposure time T perA-scan varies from 42 to 512 µs. Because of about 10 µsdead time of the camera, the shortest acquisition time is 32 µs,whereas the shortest eye exposure time is 42 µs. For longerexposure time this discrepancy becomes negligible.

For both model and in vivo measurements the opticalpower impinging on the object was 190 µW. Just fordemonstration purposes, in two retinal experiments (figure 2),the optical power was increased to 750 µW, i.e. to the level usedin the commercial instrument StratusOCT [26], still within theANSI exposure limit for continuous beam viewing [27]. Thepower in both arms was regulated by inserting the calibratedneutral density filters.

The images of various details of the normal humaneye are obtained by examining the eye of one of theauthors (25 years old, female). A standard ophthalmologicexamination confirmed the eye to be free of pathologies. Thesubjects with pathological eyes were examined by the sameinstrument transferred to Collegium Medicum of NicolausCopernicus University in Bydgoszcz (Poland). The study wasapproved by the Ethics Committee and a written informedconsent was obtained from all subjects.

3. Theory

In SOCT a recorded signal G(ω) is a product of spectrum S(ω)

of a light source and interference fringes. The signal from anobject built of two interfaces (1 and 2), e.g. a glass slide, isexpressed by

G(ω) = S(ω)(R1 + R2 + 2√

R1Rref cos(ωτ1,ref)

+2√

R2Rref cos(ωτ2,ref) + 2√

R1R2 cos(ωτ1,2)). (1)

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A Szkulmowska et al

(a) (b)

Figure 2. SOCT images of the human retina in vivo (healthy volunteer). The images were taken with (a) 256 µs/A-scan and(b) 32 µs/A-scan. In both cases the optical power incident on the cornea of 750 µW was chosen to be the same as in the commercial OCTsystem [26]. Coherent noise components are clearly visible in the top of the panel (a), whereas for (b) the shot noise is dominant.ILM—inner limiting membrane, IS/OS—photoreceptor inner/outer segment junction and RPE—retinal pigment epithelium. Arrowsindicates the equal optical distances.

The fringes originate from the interference of the referencebeam (the effective reflectivity of the reference mirrorincluding all losses introduced by a neutral density filter isRref) and the waves reflected at structural interfaces of theobject (with reflectivities of Rk). τi,k—denotes time delaybetween two waves reflected at the ith and kth location andis proportional to the optical path difference. The non-sampledependent terms are omitted in equation (1) because they canbe conveniently subtracted. The inverse Fourier transform ofequation (1),

gs (τ ) = �(τ) ⊗ (δ(τ )(R1 + R2) + 2√

R1Rrefδ(τ ± τ1,ref)

+2√

R2Rrefδ(τ ± τ2,ref) + 2√

R1R2δ(τ ± τ1,2)), (2)

contains Dirac’s deltas δ at positions corresponding to thedistances between the reflecting interfaces, and the coherencefunction of the light �(τ) = FT −1(S(ω)) which determinesthe axial resolution. Symbol ⊗ denotes the convolutionoperation. The first term in equation (2) produces a weakautocorrelation signal (because the relations Rref � Rk musthold to achieve the shot noise limit) at τ = 0. The twonext terms, which result from the interference of the objectand reference beams, contain the essential information on thelocations of structural interfaces of the object with respect tothe reference mirror position. The delta of the last term iscentred somewhere within the range 0 < τ < nl/c (l is athickness of the object, n is the refractive index of the object).

The last term in equation (2) is a parasitic one,because in a case of larger number of interfaces within theobject, the internal cross-correlations between them may addunpredictable artificial features to the image. In most instancesthese terms are hidden under the shot noise but in certainconditions they have enough intensity to be observed in theimage.

The most prominent example of such an artefact in retinalimaging is a result of cross-correlation of waves originatingfrom two strongly reflecting layers in the retina: ILM and RPE.For most experimental arrangements, this signal produces aline located within the area of the vitreous of the eye. Under

certain circumstances it may be misinterpreted as an unknownmorphological structure of the vitreous.

To demonstrate how the total exposure influences thevisibility of the cross-correlation images, two images of thesame retina are compared (figure 2). Even for the eyeexposures which are 10 times lower than in the commercialinstrument (750 µW and 256 µs with respect to 750 µW and2.5 ms) several parasitic cross-correlations produce artificialfeatures especially visible above the left part of the retinalsurface (figure 2(a)). It is easy to verify that distances betweenILM and structures around RPE match distances betweenposition τ = 0 and corresponding artefacts. The 16-foldreduction of the energy results in a strong suppression of theartefacts (figure 2(b)). Under these circumstances the essentialfeatures of the retina are still clearly recognizable and theouter/inner photoreceptor (OP/IP) layer, which is regarded asan indicator of high quality of the image is still distinguishable.

In the following paragraph we shall briefly determine thelight power that should be used to ensure that the ILM–RPEcross-correlation signal stays under the shot noise level.

The ratio of the ILM–RPE cross-correlation signal to thetotal shot noise may be expressed as [15]

S

N= ρT P0

e−R2κ

(Rref + 2R), (3)

where ρ = e−η/hν is the efficiency of photoelectricconversion of the CCD detector, e−—the electron charge,η—the total efficiency of the spectrometer, h—Planck’sconstant, ν—the central optical frequency, T —the exposuretime needed to register one A-scan, P0—the optical powerof the beam entering the interferometer, κ—the double pathcoupling ratio of the beam splitter and Rref is the effectivereflectivity of the reference mirror. Reflectivities of ILM andRPE are assumed to be the same and are denoted by R. It is alsoassumed that the condition of the shot noise limited detectionis achieved (i.e. the total optical energy nearly saturates theCCD sensor).

Plots of the SNR of the cross-correlation terms asa function of sample reflectivity calculated according to

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Coherent noise-free ophthalmic imaging by spectral optical coherence tomography

Figure 3. SNR of the parasitic cross-correlation terms versusreflectivity of the sample calculated from equation (4) for differentvalues of exposure time. Inset shows the maximal exposure timeswhich do not lead to the cross-correlation artefacts arising fromreflections at two interfaces of reflectivities R.

equation (3) are shown in figure 3. For these calculationswe assumed the value of input optical power P0 = 1 mW (theincident power on the sample was 190 µW), the double pathcoupling ratio κ = 0.20, the spectrometer efficiency η = 0.14and the double path losses associated with collimating, backcoupling to the fibre and passing through X-Y scanner to be90%. The analysed range of reflectivities covers the typicalvalues of retinal reflectivity, i.e. −48 dB and −62 dB. The insetof figure 3 presents this data in a more convenient fashion. Iftwo layers of strong and known reflectivity (here it is assumedthat both reflectivities are equal) are present in the structureone can obtain the maximum exposure time which ensures thatcross-correlation signal from these layers does not produce theartefact in the tomogram.

The most reflective layers in the retina are ILM andRPE. The values of reflectivity of these layers may beestimated using refractive index from a standard Gulstrandeye and the scattering coefficient of the retina known fromthe literature [28] as RILM = 2.75 × 10−5 (−45.6 dB) andRRPE = 3.3 × 10−5 (−44.8 dB). The additional losses causedby defocusing and aberrations of the eye and the scanningsystem are approximated as additional −10 dB. We shall thenassume that the effective reflection coefficients of all retinallayers are somewhere in between −55 dB for the stronglyreflecting structures and −60 dB for the weakly reflectingstructures.

As follows directly from equation (3), in order to keepthe ILM–RPE cross-correlation parasitic signal under the shotnoise, the initial power of the beam has to fulfill the followingcondition:

P0 <e−

ρT

Rref + 2R

R2κ. (4)

The optical power at which the cross-correlation signal is equalto the shot noise level versus exposure time, is calculated usingequation (4). The optimal region to perform an experimentand avoid a parasitic cross-correlation from two surfaces ofreflectivity R is just below the line corresponding to theparticular reflectivity. In such a condition the SOCT instrument

Figure 4. Graphical presentation of the experimental parameters:input optical power and exposure time, at which cross-correlationsignal is equal to the shot noise level. The lines correspond to twoarbitrary surface reflectivities −55 dB and −60 dB.

is optimized for the maximal sensitivity. Further increaseof either optical power or exposure time will produce a riskof parasitic cross-correlations. On the other hand decreaseof these parameters will cause reduction of sensitivity. Ifboth surfaces exhibit different reflectivities, the optimal setof parameters is somewhere between two lines in figure 4. Forsuch values the sensitivity of the SOCT device will vary from87 to 98 dB, which is sufficient for clinical studies.

4. Model experiment

In order to check the formulae derived in the previous sectiona glass slide is used as an object. The effective reflectivityof each air–glass interface, including attenuation of the neutraldensity filter placed in front of the glass slide is estimated to be−55 dB. During the first series of experiments the acquisitiontime is varied from 32 to 512 µs. The intensity at the objectarm is kept constant at 190 µW, whereas the reference intensityis adjusted to operate near the saturation level of the sensor foreach exposure time. Under such conditions the total energyof registered light and consequently the shot noise level is thesame in the whole series.

Figure 5(a) shows SOCT tomograms of a glass slide. Theglass–air interfaces are visible at the 175th and 315th pixel.At exposure time between 64 and 128 µs, the parasitic stripeemerges at the 140th pixel. Its distance from the zeroth pixelis then equal to the optical thickness—expressed in pixels—of the glass plate. Therefore, the position of this stripeconfirms that it originates from the cross-correlation betweenwaves reflected at both air–glass interfaces. The exposuretime at which the artefacts seem to be of the order of thenoise as determined experimentally correlates with theoreticalconclusions expressed graphically (figure 5)—for the samplereflectivity of −55 dB the point of S/N = 0 dB corresponds to100 µs of exposure time.

In the second series of the experiments the exposure timeis kept at 32 µs, whereas the effective reflectivity of the objectis simulated with the neutral density filters (figure 5(b)). The

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A Szkulmowska et al

(a) (b)

Figure 5. SOCT images of a glass slide obtained with (a) different acquisition time and invariant reflectivities of the object, (b) the sameacquisition time but effective reflectivities of the object were adjusted by a natural density filter. In both experiments light intensity at theobject is 190 µW, light intensity in the reference arm is adjusted to keep the total light energy per A-scan constant, near the sensor saturationlevel.

(a)

(b)

Figure 6. SOCT images of the pathological retina of the human eye in vivo. (a) Macular hole and (b) glaucomatous cupping of the opticdisc. Bars represent 300 µm in each direction.

parasitic stripe emerges from the shot noise around the air–glass effective reflectivity of −50 dB. This result is also inagreement with theoretical predictions displayed in figure 3.

5. Clinical application

The findings of the previous chapters were applied to optimizethe SOCT instrument parameters for clinical examinations. Atotal 67 eyes of 44 patients were examined in the Clinic ofOphthalmology, Collegium Medicum, Nicolaus CopernicusUniversity. In figure 6 the examples of coherent noise-freetomograms of retina are demonstrated. The following cross-sectional images are obtained with procedures that reduce theinfluence of all cross-correlation terms; those, which originatefrom the interference of waves reflected within the object, arereduced by optimization of exposure time and optical powervalues. Those from interference of waves reflected at opticalsurfaces are removed by background subtraction described inthe previous sections.

The tomogram of the human macula of a young malesuffering from traumatic macular hole is shown in figure 6(a).SOCT helps to differentiate the full thickness of the macularhole from the pseudohole. The full retinal thickness openingin the central fovea as well as some cystic changes in theneurosensory retina are clearly visible. From the SOCTtomogram presented in figure 6(b), the architecture of thepathological optic disc can be easily assessed. The tomogramwas taken slightly above the papilomacular axis in order tovisualize blood vessels. The cup of the optic disc of a personsuffering from glaucoma is much wider and deeper than thatof a healthy subject. This corresponds with clinical diagnosisof glaucomatous cupping.

6. Conclusions

In conclusion, we have demonstrated that there is an upperlimit of object exposure above which SOCT images sufferfrom coherent noise artefacts. In ophthalmic applications this

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Coherent noise-free ophthalmic imaging by spectral optical coherence tomography

level is below the ANSI safety limit. Intuitively, following theaccumulated experience from TdOCT, it is expected that SOCTophthalmic images taken close to the safety limit will alsoexhibit the best SNR. Unfortunately, under these conditions,correlated noise artefacts arise, and may be misinterpretedas real morphological elements. Therefore it is prudentto optimize the SOCT instrument parameters to keep theseparasitic terms under the shot noise. The limitation imposedon the exposure (optical power × exposure time), implies afundamental limitation to the dynamic range and sensitivity ofthe SOCT technique, leading to a trade-off between clarity ofimage and freedom from artefacts. The example quoted hereare those pertaining to the highest RPE and ILM reflectivitiesthat we have observed. In spite of this limitation, it was stillpossible to choose optimal exposure time, power and efficiencyof the device to perform imaging with a sensitivity higherthan 90 dB. For lower reflectivities than these, the specificrecommendations made here are still practical; for higherreflectivities the limit will need recalculating.

Acknowledgments

Authors would like to acknowledge the support of the grantfrom Polish State Committee for Scientific Research. One ofthe authors, TB, gratefully acknowledge the support from thegrant from Polish Science Foundation.

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